As an alternative to the boundary conditions of Problem 4.5, consider the thin fin shown in Fig….

As an alternative to the boundary conditions of Problem 4.5,
consider the thin fin shown in Fig. P4.6. Derive the temperature distribution
for this fin as

Subsequently, derive the heat transfer rate expression at x
= 0 and ‘. Also, locate the plane, a value of x, in terms of T1, T2,
T1, m and ‘ where the temperature gradient dT/dx = 0. Show that the
foregoing temperature distribution reduces to Eq. (4.92) when the value of T2
is such that dT/dx = 0 at x =t ‘.

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As an alternative to the boundary conditions of Problem 4.5,
consider the thin fin shown in Fig. P4.6. Derive the temperature distribution
for this fin as

Subsequently, derive the heat transfer rate expression at x
= 0 and ‘. Also, locate the plane, a value of x, in terms of T1, T2,
T1, m and ‘ where the temperature gradient dT/dx = 0. Show that the
foregoing temperature distribution reduces to Eq. (4.92) when the value of T2
is such that dT/dx = 0 at x =t ‘.

In a cryogenics multifluid heat exchanger, offset strip fins
are generally used between plates, In neighboring channels, different fluids
with different heat transfer coefficients and temperature differences (Th
-Tc) flow. Consider a typical fin of length ‘ as shown in Fig. P4.5.
Derive the temperature distribution in this fin as follows.

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